The Maclaurin symmetric mean (MSM) can capture the interrelationship among the multi-input arguments and it also can generalize most of the existing operators. Now MSM has been extended to intuitionistic fuzzy sets (IFSs) which can easily express the vague information. However, the operational rules of IFSs used in the extended MSM operator didn’t consider the interaction between the membership function and non-membership function, so there are some weaknesses. In this paper, in order to combine the advantages of the MSM and interaction operational rules of IFSs, we propose the intuitionistic fuzzy interaction Maclaurin symmetric mean (IFIMSM) operator, the intuitionistic fuzzy weighted interaction Maclaurin symmetric mean (IFWIMSM) operator, respectively. Furthermore, we research some desirable properties and some special cases of them. Further, we develop a new method to deal with some multi-attribute group decision-making (MAGDM) problems under intuitionistic fuzzy environment based on these operators. Finally, an illustrative example is given to testify the availability of the developed method by comparing with the other existing methods
